Why didn't you simply swap the halogen bulb with a LED replacement?
I looked into this earlier this year but was put off by reports that if the LED bulb light source is not in the correct position to be properly focused by the reflector and lens then the LED may be no better or even worse.
that is a legitimate concern; there are two aspects to it:
First the emitter may be in the wrong location w.r.t to the original filament. This will cause the effect of a parabolic type reflector to be not as intended. However if the position of the bulb can be altered, this can be mitigated to some extent.
Second, a typical filament bulb emits strongly in all directions; a significant amount of the light is thrown backwards and is reflected forwards by the reflector. However with an LED 'bulb' the light is typically thrown forwards only, because the LED device is mounted on a flat substrate. With a typical parabolic reflector, this leaves a 'hole' in what would normally be a focused beam. However provided the focus is adjustable, a satisfactory beam can usually be obtained.
This means that for example with maglites, the beam is far from perfect with an LED drop in bulb, but can usually be adjusted to be satisfactory. I'd image that the same is true of most bike lights provided you can adjust the focus.
In comparable lamps that are designed to accept LED bulbs from the start, the shape of the parabola is different, so that the focal point of the parabola is only a little way above the reflecting surface; this allows the entire reflecting surface to be illuminated (in a way that is impossible with conversions) and allows a good beam to be made.
Bike lights are different to this, in that the ideal beam isn't a focused beam from a parabola anyway. Usually it is a 'suck it and see' business; with more light available the beam shape doesn't have to be perfect.
However a decent LED light (more powerful and with a better beam shape) is now only about £15 so why bother with an LED conversion (that is almost the same price) anyway...?
cheers